Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#386 ⋊ C2 |
| Sylow | C7 ⋊ #2697 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#386 | C2 |
| prime radical | C2×#6500 | C2 |
| hypercenter | #386 | D7 |
| hypocenter | C7 | #2697 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #386 | |
680 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=e,b^a=bef,c^a=cf,d^a=de,h^a=h^6,c^b=cg,d^b=def,h^d=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13560715, #13560722, #13560831, … |
| maximal normal subgroup of | #13560715, #13560722, #13560831, … |
| maximal quotient of | #13281078, #13281196, #13281198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 7135);